9 research outputs found
Instabilities of dispersion-managed solitons in the normal dispersion regime
Dispersion-managed solitons are reviewed within a Gaussian variational
approximation and an integral evolution model. In the normal regime of the
dispersion map (when the averaged path dispersion is negative), there are two
solitons of different pulse duration and energy at a fixed propagation
constant. We show that the short soliton with a larger energy is linearly
(exponentially) unstable. The other (long) soliton with a smaller energy is
linearly stable but hits a resonance with excitations of the dispersion map.
The results are compared with the results from the recent publicationsComment: 20 figures, 20 pages. submitted to Phys. Rev.
Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
We consider, by means of the variational approximation (VA) and direct
numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D
and 3D condensates with a scattering length containing constant and
harmonically varying parts, which can be achieved with an ac magnetic field
tuned to the Feshbach resonance. For a rapid time modulation, we develop an
approach based on the direct averaging of the GP equation,without using the VA.
In the 2D case, both VA and direct simulations, as well as the averaging
method, reveal the existence of stable self-confined condensates without an
external trap, in agreement with qualitatively similar results recently
reported for spatial solitons in nonlinear optics. In the 3D case, the VA again
predicts the existence of a stable self-confined condensate without a trap. In
this case, direct simulations demonstrate that the stability is limited in
time, eventually switching into collapse, even though the constant part of the
scattering length is positive (but not too large). Thus a spatially uniform ac
magnetic field, resonantly tuned to control the scattering length, may play the
role of an effective trap confining the condensate, and sometimes causing its
collapse.Comment: 7 figure
Derivation of the equation for an ultrashort pulse in a fibre
Pulses propagating in a non-linear dispersive (glass) fibre can be described by the non-linear Schrödinger equation il the pulse is longer than a picosecond; for shorter pulses, this equation must be extended. In this paper we systematically derive this extended equation using the method of multiple scales. By using an inherent freedom in the method of multiple scales, a technique is developed such that perturbation terms are greatly simplified. The limits of validity of the derived equation are discussed. It is shown to be valid for pulses longer than 30 fs.
Self-similar parabolic optical solitary waves
We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE